By Ramón Emilio De Jesús Grullón

A bird’s eye view on energy resilience

In recent years, there has been a significant increase in the frequency and intensity of large-scale power failures, triggered by severe weather phenomena. Such occurrences have inflicted considerable damage and caused widespread disruption, leaving millions of individuals without access to electricity for prolonged periods.  For instance, the impact of Hurricane Irma in Puerto Rico (2017) was substantial, leaving over 6.7 million electrical customers without access to power at its peak. These events serve as stark reminders of the significant vulnerabilities and shortcomings in power grid infrastructure, particularly in the face of extreme weather events and need to improve its reslience. [1]

Fig 1 – Unexpected events in a power grid [10]

Historically, power systems have been designed to safeguard against routine disruptions resulting from equipment failures, human errors, and external interferences, which are characterized as Low-Impact High-Probability (LIHP) events. These conventional protection measures have largely succeeded in maintaining an acceptable level of power delivery reliability for local customers, with a primary focus on ensuring continuity of service. However, the increasingly frequent occurrence of High-Impact Low-Probability (HILP) events, such as extreme weather phenomena, has highlighted the need for more comprehensive protection strategies and research on what are the fundamentals issues that govern energy resilience, and how to improve it. 

 IEEE standard reliability indices in the Dominican Republic
Fig. 2 – IEEE standard reliability indices in the Dominican Republic Distribution Energy Utilities (JUL 2021) – System Average  Interruption  Frequency  Index  (SAIFI)  and System  Average  Interruption  Duration  Index  (SAIDI) and Customer Average Interruption Duration Index (CAIDI) Source: Superintendencia de Electricidad (SIE)

From Reliability to Energy Resilience – The fundamentals.

Resiliency is defined as “the ability to prepare for and adapt to changing conditions and withstand and recover rapidly from disruptions”[2]The concept of resilience represents a departure from the traditional approach to reliability, which focuses on the frequency and duration of failures event-agnostically and situational awareness and diagnosis, resilience seeks to track the dynamics, and incorporates reactive actions against contingencies, such as launching restoration operations and ensuring the continued functionality of critical loads.

Power System Engineers are familiar with IEEE standard reliability indices: System Average Interruption  Frequency  Index  (SAIFI)  and System  Average  Interruption  Duration  Index  (SAIDI). (See Figure 2). Reliability metrics are useful means of assessing the impact of recurrent events that have available historical records, and for which maintenance actions can be taken. However, major hazards, such as severe weather events, are typically excluded from these metrics. In an effort to capture the impact of more severe events, researchers have proposed extending some of these metrics, including the Storm Average Interruption Frequency Index (STAIFI) and the Storm Average Interruption Duration Index (STAIDI). Nevertheless, it has been demonstrated that these two metrics are not suitable for evaluating power system resilience because they tend to show large deviations that can even exceed the thresholds. [3]

As interest in power system resilience continues to expand, there is a growing body of literature on quantitative assessments of resilience that propose relevant indicators to guide cost-benefit studies prior to investment planning. However, quantifying the multidimensional characteristics of resilience presents a significant challenge that requires a multidisciplinary approach that considers spatio-temporal scales, characterization of the performance and operational aspects of the power grid.

Taxonomy of resilience evaluation methods and metrics

State-of-the-art resilience frameworks for power distribution networks could be classified, evaluated, and compared using the taxonomy in figure 3[1] .The type of analysis will vary depending on the objective and the state (see figure 4) of grid conditions under the event.

Classification for resilience evaluation frameworks
Fig. 3 – Classification for resilience evaluation frameworks

Numerous resilience features are inherent in the performance curve depicted in Figure 4, also known as the Resilience Trapezoid. This is because constructing such a graph involves considering all the factors that come into play during a catastrophic contingency.

The vertical axis and horizontal axes represent the grid functionality and the time, respectively. The grid is under normal conditions, QN, before an extreme weather event occurs at time tE. An extreme weather event occurs at time tE and causes the grid functionality to degrade, until it stops at time tD, when the grid is considered at its worst condition Q(tD). This state will remain constant if no restoring actions are carried out, shown in Figure 4 (below) as the degraded state. [4]

The resilience triangle  (b) the resilience trapezoid
Fig. 4 – (a) The resilience triangle  (b) the resilience trapezoid

Grid resilience indices

Resilience metrics come in many different forms, but they can generally be grouped into one of two categories: attribute-based and performance-based metrics. Attribute-based metrics generally try to answer the question “What makes my system more/less resilient?” and can be used to provide a   baseline understanding of the system’s current resilience, relative to other systems. While Performance-based metrics are generally quantitative approaches for answering the question “How resilient is my system?” These methods are used to interpret quantitative data that describe infrastructure outputs in the event of specified disruptions and formulate metrics of infrastructure resilience. [5]

Various methodologies for quantifying the resilience index have been proposed by researchers in the field using the Resilience Trapezoid.  [4]

Henry and Ramirez-Marquez [6] conducted a comparative analysis of the increase in grid functionality from the damaged state with the decrease in functionality from the normal state. The attainment of complete resilience is indicated when the restored grid functionality matches the normal (pre-event) functionality. This relationship is mathematically described as follows:

Where RQ(t) is the resilience index for grid functionality. The speed of restoration is not considered in this index.

Francis and Bekera [7] proposed a framework to evaluate the resilience metric that considers the recovery time and system states. The normalization of the damaged and restored states of the system is based on their stable state. The equation to calculate the resilience metric in this framework can be expressed as follows:

Here, Q(tR), Q(tD), and Q(tE) represent the grid functionality at the restored, damaged, and normal condition, respectively. This index accounts for the absorptive, adaptive, and restorative capacity of the grid, and provides a comprehensive measure of its resilience.

Sp is the recovery speed index and is expressed by the following equation:

In a study by Ouyang et al. [8], the resilience index was calculated as the ratio of the actual performance of a system to its target performance, ranging from 0 to 1. This metric considers parameters such as the flow or services delivered, availability of critical facilities, number of customers served, or support of economic activities. The grid resilience can be mathematically expressed using the following equation:

Where Rinst is the instantaneous grid resilience index. Qactual(t) is the actual grid functionality, Qtarget(t) is the target grid functionality, and Tis the observation period.

Shinozuka et al. [9] proposed a two-fold approach to measure grid resilience, which encompasses physical hardiness and operational capability.

Rphysical and Roperational define the physical hardiness and operational capacity during both the degradation and restoration stages. The time of completed restoration and at the worst damaged condition are marked by the variables tR and tD, respectively. The grid’s physical hardiness index is derived by assessing the degree of functionality that the grid can retain during the event. The operational capability index, on the other hand, incorporates the amount of service recovered from the damaged condition and the duration of restoration required for the same.

Open Issues and Challenges

The energy grid is a complex and dynamic system with multiple interdependent components that exhibit intricate behavior over time. Hence, devising frameworks and metrics to measure the response and recovery of the system to adversarial events poses a challenging task. Despite the strides made in the research on performance measures, there remains a lack of metrics that consider all three intrinsic characteristics of the grid at the system level: the spatiotemporal nonstationary failure-recovery, weather variables, and the influence of service providers, customers, and the community at large.

The following research questions relating to resilience metrics arise: [3]

  • What resilience metrics can provide a cohesive representation of these factors?
  • What approaches  can  lead  to  such  resilience  metrics at  the  system  level,  combining  weather  with  failure–recovery–impact processes?
  • What (additional) data are needed to evaluate resilience of the infrastructure and services?

Answers to these questions are anticipated to arise from the formulation of system-wide metrics and models that incorporate the relevant variables from a bottom-up approach. Additionally, extensive data analytics are necessary to derive the values of newly developed metrics and compare them with established standards.


[1]        Y. Nait Belaid et al., “Resilience Quantification of Smart Distribution Networks-A Bird’s Eye View Perspective,” 2021, doi: 10.3390/en14102888ï.

[2]        “Presidential Policy Directive — Critical Infrastructure Security and Resilience |” (accessed Mar. 27, 2023).

[3]        C. Ji, Y. Wei, and H. V. Poor, “Resilience of Energy Infrastructure and Services: Modeling, Data Analytics, and Metrics,” Proceedings of the IEEE, vol. 105, no. 7, pp. 1354–1366, Jul. 2017, doi: 10.1109/JPROC.2017.2698262.

[4]        F. H. Jufri, V. Widiputra, and J. Jung, “State-of-the-art review on power grid resilience to extreme weather events: Definitions, frameworks, quantitative assessment methodologies, and enhancement strategies,” Applied Energy, vol. 239. Elsevier Ltd, pp. 1049–1065, Apr. 01, 2019. doi: 10.1016/j.apenergy.2019.02.017.

[5]        E. Vugrin, A. Castillo, and C. Silva-Monroy, “SANDIA REPORT Resilience Metrics for the Electric Power System: A Performance-Based Approach.” [Online]. Available:

[6]        D. Henry and J. Emmanuel Ramirez-Marquez, “Generic metrics and quantitative approaches for system resilience as a function of time,” Reliab Eng Syst Saf, vol. 99, pp. 114–122, Mar. 2012, doi: 10.1016/J.RESS.2011.09.002.

[7]        R. Francis and B. Bekera, “A metric and frameworks for resilience analysis of engineered and infrastructure systems,” Reliability Engineering and System Safety, vol. 121. Elsevier Ltd, pp. 90–103, 2014. doi: 10.1016/j.ress.2013.07.004.

[8]        M. Ouyang and L. Dueñas-Osorio, “Multi-dimensional hurricane resilience assessment of electric power systems,” Structural Safety, vol. 48, pp. 15–24, May 2014, doi: 10.1016/J.STRUSAFE.2014.01.001.

[9]        C. S. C. T. F. M. O. T. S. M. et al. Shinozuka M, “Resilience of integrated power and water systems. Seism Eval Retrofit Lifeline Syst:65–86,” pp. 65–68, 2003.

[10]      A. M. Amani and M. Jalili, “Power Grids as Complex Networks: Resilience and Reliability Analysis,” IEEE Access, vol. 9, pp. 119010–119031, 2021, doi: 10.1109/ACCESS.2021.3107492.

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PI – Ramón Emilio De Jesús Grullón

This article is derived from the Subject Data funded in whole or part by NAS and USAID under the USAID Prime Award Number AID-OAA-A-11-00012. Any opinions, findings, conclusions, or recommendations expressed in this article are those of the authors alone and do not necessarily reflect the views of USAID or NAS.

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